This report provides an exploratory analysis of juvenile snowshoe hares in the Bonanza Creek forest in Tanana Valley Alaska. The data was observed and recorded from 1999 - 2012. The hares were observed in three different locations: Riparian Forest (bonrip), Mature Forest (bonmat), Lowlands Black Spruce Forest (bonbs). Bonrip is a flood zone, Bonmat is a mature black spruce forest, and Bonbs was the site used for live trapping the snowshoe hares for monitoring. The following report includes an analysis of the number of juvenile hare trappings conducted each year of the study, an analysis of the relationship between site and gender on average hare weight, and linear regression analysis of the relationship between hare weight and the hind foot length.
Dr. Knut Kielland (Kielland et. al. 2017.) was the principal investigator for this project. This dataset includes information on the trappings of both adult and juvenile hares at all 3 sites including date, trap number, and ear tag identifier. In addition, the dataset contains information on each hare trapped, including sex, weight, hind foot length, and age. In this report, a two-sample unpaired t-test with an \(\alpha\) = 0.05 was used to compare the average weights between male and female juvenile hares. Differences between groups are described by Cohen’s d effect size. A simple linear regression was used to model the relationship between hare weight and hind foot length. All analyses are on R Version 4.1.1 using RStudio Version 1.4.1717.
Figure 1. Histogram of juvenile hare trappings in Bonanza Creek from 1998-2012, from Kielland et al. (2017). Over the duration of the study, the trappings per year remained inconsistent.
Trappings Analysis
The minimum number of trappings each year, 2, occurred in 2002, and the maximum number of trappings each year, 126, occurred in 2009. The average amount of trappings performed each year over the entire project was 31.5 and the median was 18.5. There does not seem to be a consistent or trending number of trappings from year to year. There are several factors that could be affecting the trapping rates such as the number of days and the number of traps each year in the study. This could be due to researcher effort, difficulty trapping younger hares, or even seasonal variability in juvenile hare presence in those locations. In order to standardize the juvenile hare population moving forward, researchers should conduct the study at the same time each year, and place the same number of traps from year to year.
Figure 2. Bar plot of male (purple), female (pink), and the unknown sex (gray) juvenile hare weights by site in Bonanza Creek from 1998-2012, from Kielland et al. (2017). The error bars are representative of the standard deviation of the sample weights. The unknown genders are represented by NA.
Weight by Sex & Site Analysis
As Figure 2 shows, the female juvenile hares have a lower average weight compared to males at every location. At the Bonanza Lowland location, the females average weight is 1022.06 \(\pm\) 292.96 grams compared to the male average weight of 1073.08 \(\pm\) 222.64 grams. The NA bar column does not show up in this site because there isn’t enough data to calculate a mean weight. At the Bonanza Mature site, the female average weight is 808.19 \(\pm\) 361.12 grams compared to the male average weight of 950.12 \(\pm\) rweight_sex_site$sd_weight[5]`grams and the unknown sex hare average weight of 816.67 \(\pm\) 307.09 grams. Finally, at the Bonanza Riparian site, the female average weight is 824.15 \(\pm\) 255.04 grams compared to the male average weight of 929.27 \(\pm\) 349.17grams and the unknown sex hare average weight of 372 \(\pm\) 258.79 grams.
| Sex | Mean Weight (g) | Standard Deviation(g) | Sample Size (n) |
|---|---|---|---|
| f | 855.4 | 292.3 | 200 |
| m | 945.9 | 333.2 | 163 |
Weight by Sex Analysis (NAs Excluded)
The actual difference in these means is 90.5 grams. The mean weight of female hares across all three sites is 855.4 \(\pm\) 292.3 grams and the male hares average weight across all sites is 945.9 \(\pm\) 333.2 grams. A standard unpaired two sample t-test was conducted to analyze if the calculated difference is statistically significant. The test resulted in a p-value of 0.007 (effect size, 0.2905), and means there is a 0.709% chance that these samples would have a difference in means at least as different as 90.5 grams, assuming that the two samples are drawn from populations with the same mean. The null hypothesis is that the difference in the means between males and females is equal to 0, while the alternative hypothesis is that the difference in means is not equal to 0. Therefore with this p-value, the null hypothesis is rejected because it falls below the assigned significance level of (\(\alpha\) = 0.05).
Figure 3. Linear regression model scatterplot showing length of juvenile weight (g) as a function of hind foot length (mm). The dots are representative of individual juvenile hare observations. The blue line plotted across the dots represents a simple linear regression. Data: (Kielland et al. 2017).
Linear Regression of Hind Foot & Weight Analysis
The relationship between juvenile hare weight and hind foot length is described by the linear regression model displayed by Figure 3. The linear regression model suggests that hind foot length affects weight (p < 0.001, R2 = 0.3) with the average slope of \(\beta\) = 9.52 g/mm. According to the Pearson’s r test, the correlation between hind foot and weight is significant and positive (Pearson’s r = 0.55, p < 0.001). Although these p-values suggest significance, it is concerning that the assumption of homoscedasticity in the linear regression is not accomplished. Therefore, performing a linear regression is not an appropriate method of determining the relationship between hind foot length and weight.
Kielland, K., F.S. Chapin, R.W. Ruess, and Bonanza Creek LTER. 2017. Snowshoe hare physical data in Bonanza Creek Experimental Forest: 1999-Present ver 22. Environmental Data Initiative. https://doi.org/10.6073/pasta/03dce4856d79b91557d8e6ce2cbcdc14